The HCF of 48 and 54 is 6. HCF stands for Highest Common Factor, and as the name suggests, the number that is highest among the common factors is known as HCF. It can also be referred to as GCD, Greatest Common Divisor or GCF, Greatest Common Factor. For the given set of numbers 48 and 54, 6 is the HCF/GCD/GCF. Even though there are other common factors 1, 2, and 3, 6 is greater than the other common factors. You can refer to the HCF and LCM to understand the difference between them.
What is the HCF of 48 and 54?
The Highest Common Factor, also known as the Greatest Common Factor, of 48 and 54 is 6.
How to Find HCF of 48 and 54?
There are three methods to find the HCF of 48 and 54:
- Prime Factorisation
- Long Division method
- Listing common factors
HCF of 48 and 54 by Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 48 and 54 can be expressed as:
48 = 2 × 2 × 2 × 2 × 3
54 = 2 × 3 × 3 × 3
Common prime factors are 2 and 3. Therefore, HCF will be
HCF (48, 54) = 2 × 3 = 6.
HCF of 48 and 54 by Long Division Method
In the Long Division method, the below steps are followed.
- From the given set of numbers, the smallest number becomes the divisor, and the larger number becomes the dividend.
- In the next step, the smaller number becomes the dividend, and the remainder becomes the divisor.
- The above step is followed until the remainder is zero.
- The last divisor would be the HCF.
For 48 and 54, the HCF by long division method is:
Hence, HCF (56, 84) = 6
HCF of 48 and 54 by Listing Common Factors
By listing all the factors of given numbers, we can identify the Highest/Greatest/Biggest common factor, which is the HCF. Below is the list of factors for 48 and 54:
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
Therefore, HCF (48, 54) = 6
Related Articles
Video Lesson on Properties of HCF and LCM
Solved Examples
1. Find the second greatest number that divides 48 and 54 evenly.
The common factors of 48 and 54 are 1, 2, 3 and 6. The second greatest number that divides 48 and 54 evenly is 3.
2. What is the GCF of 5 and 5?
The GCF of 5 and 5 is 5.
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